Cascade of fractional quantum Hall states in two-dimensional system

Abstract The observation of fractional quantum Hall (FQH) effect in two-dimensional electron gases ushered in the investigations of topological phases driven by strong electron correlations. Their remarkable features include fractionalized elementary excitations, gapless boundary states, and nontrivial quantum entanglement patterns. Thanks to the persistent efforts of building new platforms and making higher quality samples, a diverse plethora of FQH states have been unveiled in experiments. We report a systematic study of ultrahigh quality GaAs/AlGaAs quantum wells with mobility up to ${\rm{\ 3}}{\rm{.7}} \times {\rm{1}}{{{\rm{0}}}^{\rm{7}}}{\rm{ c}}{{{\rm{m}}}^2}{{{\rm{V}}}^{ - 1}}{{{\rm{s}}}^{ - 1}}$ using quantum transport measurements in nuclear adiabatic demagnetization and dilution refrigerators down to 1 mK. In addition to many FQH states that have already been identified in previous works, new longitudinal resistance dips are observed at filling factors 17/33 and 15/31. The application of an in-plane magnetic field causes disparate variations of the FQH states. Theoretical foundation of these states is discussed in the framework of composite fermion theory. While most fractions can be explained as non-interacting composite fermions forming integer quantum Hall states, a few states correspond to FQH states of composite fermions that arise from residual interaction between them. We summarize the observed fractions in the range of 0 < $\nu $ < 2 and propose a pattern to account for their experimental appearance that provides an intuitive picture about the relative strengths of different FQH states.